Search: id:A000318
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%I A000318 M3713 N1517
%S A000318 4,128,16384,4456448,2080374784,1483911200768,1501108249821184,
%T A000318 2044143848640217088,3605459138582973251584,7995891855149741436305408,
%U A000318 21776918737280678860353961984,71454103701490016776039304265728
%N A000318 Generalized tangent numbers.
%D A000318 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000318 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000318 D. Shanks, Generalized Euler and class numbers, Math. Comp. 21 (1967), 
               689-694; 22 (1968), 699.
%H A000318 Thomas Baruchel, <a href="http://baruchel.free.fr/~thomas/">Home Page</
               a>
%F A000318 The g.f. has the following continued fraction expansion: g.f. = [4, b(0), 
               c(0), b(1), c(1), b(2), c(2), ...] where b(n) = sum(k=0, n, 1/(2*k+1))^2 
               / (128*(n+1)*x), c(n) = -4/( sum(k=0, n, 1/(2*k+1))*sum(k=0, n+1, 
               1/(2*k+1))*(2*n+3) ) and each convergent of this continued fraction 
               is a Pad'e approximant of the McLaurin series sum(k=1, \infty, a(n)*x^(n-1)). 
               - Thomas Baruchel, Oct 19 2005
%Y A000318 Equals 2^(4n-2) * A000182(n).
%Y A000318 Sequence in context: A128790 A013823 A130318 this_sequence A141367 A141368 
               A146555
%Y A000318 Adjacent sequences: A000315 A000316 A000317 this_sequence A000319 A000320 
               A000321
%K A000318 nonn,easy
%O A000318 1,1
%A A000318 N. J. A. Sloane (njas(AT)research.att.com).
%E A000318 More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jun 03 2000

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